Geometrical structure analysis of a zero-pressure-gradient turbulent boundary layer

2018 ◽  
Vol 846 ◽  
pp. 318-340 ◽  
Author(s):  
Weipeng Li ◽  
Lipo Wang
Keyword(s):  
Boundary Layer ◽  
Vector Field ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Local Extremum ◽  
Model Solution ◽  
Segment Length ◽  
Starting Point ◽  
Vector Case ◽  
Grid Points

The present work focuses on the geometrical features of a zero-pressure-gradient turbulent boundary layer based on vectorline segment analysis. In a turbulent vector field, tracing from any non-singular point, along either the vector or the inverse direction, one will reach a local extremum of the vector magnitude. The vectorline between the two local extrema is defined as the vectorline segment corresponding to the given spatial point. Specifically the vectorline segment can be the streamline segment for the velocity vector case, or the vorticity line segment for the vorticity vector case. Such a quantitatively defined and space-filling vectorline segment structure reflects the natural vectorial topology. Because of inhomogeneity in the wall-normal direction, vectorline segments corresponding to the grid points at specified wall-normal distances are sampled for statistics. For streamline segments, the probability density function (p.d.f.) of the normalized segment length in different flow regions matches a model solution, and for vorticity line segments such a p.d.f. in the log-law region and beyond matches the same model solution, which indicates some universality of different flow regions and different vector field structures. Typically the joint p.d.f. of the characteristic parameters of streamline segments presents clear asymmetry, which is closely related to the skewness of the velocity derivative. Moreover, the orientation statistics of vectorline segments, characterized by the coordinate difference between the segment starting point and ending point, have been provided to quantify the flow anisotropy.

The accelerated fully rough turbulent boundary layer

1977 ◽  
Vol 82 (3) ◽  
pp. 507-528 ◽  
Author(s):  
Hugh W. Coleman ◽  
Robert J. Moffat ◽  
William M. Kays
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Stress Tensor ◽  
Skin Friction ◽  
Shape Factor ◽  
Reynolds Shear Stress ◽  
Smooth Wall ◽  
Mean Velocity

The behaviour of a fully rough turbulent boundary layer subjected to favourable pressure gradients both with and without blowing was investigated experimentally using a porous test surface composed of densely packed spheres of uniform size. Measurements of profiles of mean velocity and the components of the Reynolds-stress tensor are reported for both unblown and blown layers. Skin-friction coefficients were determined from measurements of the Reynolds shear stress and mean velocity.An appropriate acceleration parameterKrfor fully rough layers is defined which is dependent on a characteristic roughness dimension but independent of molecular viscosity. For a constant blowing fractionFgreater than or equal to zero, the fully rough turbulent boundary layer reaches an equilibrium state whenKris held constant. Profiles of the mean velocity and the components of the Reynolds-stress tensor are then similar in the flow direction and the skin-friction coefficient, momentum thickness, boundary-layer shape factor and the Clauser shape factor and pressure-gradient parameter all become constant.Acceleration of a fully rough layer decreases the normalized turbulent kinetic energy and makes the turbulence field much less isotropic in the inner region (forFequal to zero) compared with zero-pressure-gradient fully rough layers. The values of the Reynolds-shear-stress correlation coefficients, however, are unaffected by acceleration or blowing and are identical with values previously reported for smooth-wall and zero-pressure-gradient rough-wall flows. Increasing values of the roughness Reynolds number with acceleration indicate that the fully rough layer does not tend towards the transitionally rough or smooth-wall state when accelerated.

A Superposition Analysis of the Turbulent Boundary Layer in an Adverse Pressure Gradient

1951 ◽  
Vol 18 (1) ◽  
pp. 95-100
Author(s):  
Donald Ross ◽  
J. M. Robertson
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Pressure Recovery ◽  
Stress Coefficient ◽  
Wall Shear

Abstract As an interim solution to the problem of the turbulent boundary layer in an adverse pressure gradient, a super-position method of analysis has been developed. In this method, the velocity profile is considered to be the result of two effects: the wall shear stress and the pressure recovery. These are superimposed, yielding an expression for the velocity profiles which approximate measured distributions. The theory also leads to a more reasonable expression for the wall shear-stress coefficient.

Predicting Turbulent Boundary Layer Wall Pressure Fluctuations in Adverse Pressure Gradients

2005 ◽  
Author(s):  
Frank J. Aldrich
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Pressure Fluctuations ◽  
Adverse Pressure Gradient ◽  
Wall Pressure ◽  
Prediction Tool ◽  
Pressure Gradients ◽  
Wall Pressure Fluctuations ◽  
The Difference

A physics-based approach is employed and a new prediction tool is developed to predict the wavevector-frequency spectrum of the turbulent boundary layer wall pressure fluctuations for subsonic airfoils under the influence of adverse pressure gradients. The prediction tool uses an explicit relationship developed by D. M. Chase, which is based on a fit to zero pressure gradient data. The tool takes into account the boundary layer edge velocity distribution and geometry of the airfoil, including the blade chord and thickness. Comparison to experimental adverse pressure gradient data shows a need for an update to the modeling constants of the Chase model. To optimize the correlation between the predicted turbulent boundary layer wall pressure spectrum and the experimental data, an optimization code (iSIGHT) is employed. This optimization module is used to minimize the absolute value of the difference (in dB) between the predicted values and those measured across the analysis frequency range. An optimized set of modeling constants is derived that provides reasonable agreement with the measurements.

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